The long term goal of this work is the development of methods to quantify the regional distribution of radiolabeled tracers in humans and animals. This is to be accomplished in part through the development of third generation instruments for single photon emission computed tomography (SPECT) which approach the physical limits of sensitivity and resolution. A second component of this work is devising optimal image reconstruction techniques which extract the maximum information from the data and which include corrections for attenuation, scatter, and the measurement geometry. The emphasis in this component is on iterative, discrete estimation algorithms.